Symmetry-guided scattering engineering in modular gain-loss photonic crystals

We present a systematic study of the scattering characteristics of multilayer photonic crystals composed of modular gain-loss unit cells, focusing on how stacking geometry and defect engineering govern non-Hermitian optical responses. Within PT-symmetric configurations, we reveal the simultaneous occurrence of coherent perfect absorption (CPA) and lasing, accompanied by reflectionless resonant tunneling and perfect energy balance. When PT symmetry is broken, the CPA and lasing channels decouple into distinct spectral regions, yet reciprocity preserves symmetric transmission. By tuning the stacking arrangement and complex refractive profiles, we further uncover symmetry-enabled functionalities, including a broadband all-reflecting mirror, a high-Q narrowband filter, unidirectional reflectionless transport, and cloak-like transparent windows. These results establish a unified symmetry-guided framework linking the spectral singularities of the scattering matrix to device-level functionalities, offering practical routes for the design and control of next-generation non-Hermitian photonic systems.